Washington: US President Donald Trump on Sunday denied having told a leading US daily that he shared a "good relationship" with North Korean leader Kim Jong-un, asserting that he was "falsely" quoted in the "fake news" story.

In an interview on Thursday, 'The Wall Street Journal' reported that Trump had developed a positive relationship with the North Korea's leader despite their differences.

"I probably have a very good relationship with Kim Jong-un. I have relationships with people. I think you people are surprised," Trump was quoted as saying in the interview.

Trump said the leading US newspaper knew exactly what he had said, but simply wanted "fake news".

The Wall Street Journal stated falsely that I said to them “I have a good relationship with Kim Jong Un” (of N. Korea). Obviously I didn’t say that. I said “I’d have a good relationship with Kim Jong Un,” a big difference. Fortunately we now record conversations with reporters...

...and they knew exactly what I said and meant. They just wanted a story. FAKE NEWS! — Donald J. Trump (@realDonaldTrump) January 14, 2018

Moments later, White House Press Secretary Sarah Sanders released the audio clip of the interview.

"As you know, I have a great relationship with Prime Minister Abe of Japan and I would probably have a very good relationship with Kim Jong un of North Korea," the President said in the audio.

The Wall Street Journal, however, defended its version of the interview.

File image of US president Donald Trump. AP

"We have reviewed the audio from our interview with President Trump, as well as the transcript provided by an external service, and stand by what we reported," the daily tweeted.

It also released the portion of the audio disputed by the White House.

In a subsequent tweet, Sanders said the White House had approached The Wall Street Journal on Friday for a correction, but they refused to do it.

"We first contacted the WSJ Friday morning and asked for a correction. They repeatedly refused to issue one despite clear audio evidence they'd misquoted POTUS," she tweeted on Sunday in response to a question asked on the social media site.

"So much Fake News is being reported. They don't even try to get it right, or correct it when they are wrong. They promote the Fake Book of a mentally deranged author, who knowingly writes false information.

"The Mainstream Media is crazed that WE won the election!" Trump tweeted, expressing his frustration over his coverage by the mainstream media.

Trump has ridiculed Kim in the past, calling him a "maniac" and "little rocket man".

Kim has responded by describing the US president a "mentally deranged US dotard".

Last week, Trump told South Korea's President Moon Jae-in that he was open to direct talks with North Korea on its nuclear programme.

"Sure. I always believe in talking. If something can happen and something can come out of those talks, that would be a great thing for all of humanity," he told reporters.

The president had previously dismissed the idea of direct talks with North Korea, tweeting in October that negotiations with the country were a waste of time.